Children who are born with heart defects may require prostaglandin infusion to sustain life, it allows for a source of blood flow to the lungs, or the lower extremities, depending of the type of cardiac anatomy. Infants continue on prostaglandin until surgical correction or palliation can take place. Apnea is the most significant side effect of prostaglandin infusion, often requiring intubation and mechanical respiration (breathing tube and breathing machine).The purpose of the research project is to determine whether a medication called aminophylline can prevent the side effect of lack of breathing and subsequent need for placement on a breathing machine. Aminophylline is a medication that stimulates infants to breathe, and is used extensively to help premature babies to have more stable breathing patterns. It also is used in the treatment of asthma in children. Aminophylline is FDA (Food and Drug Administration) approved for treatment of apnea in infants. By giving aminophylline at the same time as prostaglandin, we hope to prevent infants from becoming apneic (not breathing), thereby preventing the need for intubation and mechanical ventilation (breathing tube and breathing machine). No other drugs or interventions are being studied for this particular problem. Newborn infants with heart disease requiring prostaglandin therapy are targeted for this research. They are the only group of patients who will receive this medication, and therefore are the only potential group who could benefit from this type of intervention. Patients will be randomized to a treatment group and a placebo group in a double blind fashion. The expected outcome for patients receiving aminophylline is a decrease in the likelihood of apnea and subsequent intubation. Those patients in the placebo group are expected to have the normal risk of apnea, approximately 25% of patients.